Journal of Contaminant Hydrology 57 (2002) 259 – 279
www.elsevier.com/locate/jconhyd
Two-site kinetic modeling of bacteriophages
transport through columns of saturated dune sand
Jack F. Schijven a,1, S. Majid Hassanizadeh b,*,
Ria H.A.M. de Bruin a,2
a
National Institute of Public Health and the Environment, Microbiological Laboratory for Health Protection,
P.O. Box 1, 3720 BA Bilthoven, The Netherlands
b
Delft University of Technology, Faculty of Civil Engineering and Geosciences,
P.O. Box 5048, 2600 GA Delft, The Netherlands
Received 13 August 2001; received in revised form 30 November 2001; accepted 3 December 2001
Abstract
Breakthrough curves, on a semi-log scale, from tests in porous media with block-input of viruses,
bacteria, protozoa and colloidal particles often exhibit a typical skewness: a rather slowly rising limb
and a smooth transition of a declining limb to a very long tail. One-site kinetic models fail to fit the
rising and declining limbs together with the tail satisfactorily. Inclusion of an equilibrium adsorption
site does not seem to improve simulation results. This was encountered in the simulation of
breakthrough curves from a recent field study on the removal of bacteriophages MS2 and PRD1 by
passage through dune sand. In the present study, results of laboratory experiments for the study of
this issue are presented. Breakthrough curves of salt and bacteriophages MS2, PRD1, and fX174 in
1D column experiments have been measured. One- and two-site kinetic models have been applied to
fit and predict breakthrough curves from column experiments. The two-site model fitted all
breakthrough curves very satisfactorily, accounting for the skewness of the rising limb as well as for
the smooth transition of the declining limb to the tail of the breakthrough curve. The one-site model
does not follow the curvature of the breakthrough tail, leading to an overestimation of the
inactivation rate coefficient for attached viruses. Interaction with kinetic site 1 is characterized by
relatively fast attachment and slow detachment, whereas attachment to and detachment from kinetic
site 2 is fast. Inactivation of viruses and interaction with kinetic site 2 provide only a minor
contribution to removal. Virus removal is mainly determined by the attachment to site 1.
Bacteriophage fX174 attached more than MS2 and PRD1, which can be explained by the greater
*
Corresponding author. Tel.: +31-15-278-7346.
E-mail addresses: Jack.Schijven@rivm.nl (J.F. Schijven), Majid.Hassanizadeh@ct.tudelft.nl
(S.M. Hassanizadeh), Ria.de.Bruin@rivm.nl (H.A.M. de Bruin).
1
Tel.: +31-30-274-2994.
2
Tel.: +31-30-274-3929.
0169-7722/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 9 - 7 7 2 2 ( 0 1 ) 0 0 2 1 5 - 7
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J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
electrostatic repulsion that MS2 and PRD1 experience compared to the less negatively charged
fX174. D 2002 Elsevier Science B.V. All rights reserved.
Keywords: Bacteriophages; Virus transport; Column experiments; MS2; PRD1; fX174; Kinetic modeling
1. Introduction
Removal of microorganisms from water due to passage through soil is of great
importance in drinking water production. In the Netherlands, about 14% of the total
drinking water is produced from pre-treated surface water that is artificially recharged in
dune areas. No chlorination of water is applied and the adequate removal of microorganisms is for the most part dependent on the efficiency of removal by passage through
soil. Also, delineation of wellhead protection zones against microbial pollution is based on
the removal capacity of soils. There have been numerous studies to identify various
removal processes and quantify their share in overall removal of microorganisms.
Commonly, these studies involve the measurement of breakthrough curves in the field or
laboratory column experiments (see Schijven and Hassanizadeh, 2000 for an extensive
review). It is well known that kinetic adsorption is a very important process in virus
removal. Usually, an advection – dispersion model, including one-site kinetic attachment as
well as first-order inactivation, is employed to simulate measured breakthrough curves.
Often, semi-log plots of breakthrough curves from tests with block-input of viruses
(Bales et al., 1991, 1993; DeBorde et al., 1999; Dowd et al., 1998; Fujito and Lytle, 1996),
bacteria (Hornberger et al., 1992; Johnson et al., 1995; Lindqvist et al., 1994; Kinoshita et
al., 1993; McCaulou et al., 1994; Tan et al., 1994), Cryptosporidium (Harter et al., 2000)
and colloidal particles (van de Weerd et al., 1998) exhibit a typical skewness: a rather
slowly rising limb and a smooth transition of a declining limb to a very long tail. It is known
that one-site kinetic models fail to fit the rising and declining limbs together with the tail
satisfactorily (Bales et al., 1991; Harter et al., 2000; Hornberger et al., 1992; Lindqvist et
al., 1994; McCaulou et al., 1994; Tan et al., 1994). There are models where one kinetic
reversible adsorption site and one equilibrium site are assumed to be present (cf. Bales et al.,
1991; Toride et al., 1995). It is often shown that the contribution of equilibrium adsorption
to virus attenuation is negligible (see, e.g., Bales et al., 1991, 1997; Schijven and
Hassanizadeh, 2000). There are yet other models where one reversible kinetic site and
one irreversible adsorption site are assumed. For example, in one study on bacterial
transport (Johnson et al., 1995), it was shown that a model that assumed a time-dependent
detachment function and a limited number of favorable irreversible attachment sites, could
simulate the rising and climbing limbs of the breakthrough curve satisfactorily. In that
study, however, the tails were measured for a short period only. Recently, in a study on the
removal of viruses in unsaturated porous media (Chu and Jin, 2001), two kinetic adsorption
sites were considered: adsorption to soil surfaces as well as adsorption to the air – water
interface. But, the possibility of presence of two kinetic reversible adsorption sites in
saturated soil has so far not been investigated.
In the present study, we investigate the possibility that more than one type of kinetic site
may be present. Kinetic sites with different rates of attachment and detachment may exist
J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
261
due to surface charge heterogeneity of the granular medium and/or physical non-equilibrium. Patch-wise charge heterogeneities are common to all aqueous geologic settings,
originating from inherent differences in the surface properties of adjacent crystal faces on
mineral grains, and from minerals having bulk- or surface-bound chemical impurities (Ryan
and Elimelech, 1996). Physical non-equilibrium results from the exchange of particles or
solutes between mobile and immobile regions (Toride et al., 1995).
Recently, a series of field and laboratory experiments have been carried out in order to
gain insight in virus removal processes in dune sand and developing conceptual models for
quantitative modelling of these processes (Schijven, 2001). An extensive field study was
carried out in the dune area of Castricum, The Netherlands. This was aimed at investigating the effectiveness of dune recharge for virus removal (Schijven et al., 1999). Recharge
water was dosed with bacteriophages MS2 and PRD1 for 11 days at a constant
concentration in a 10 15 m compartment that was isolated in a recharge basin.
Breakthrough was monitored for 120 days at six wells with their screens located along
a calculated flow line. Concentrations of both phages were reduced about 3 log10 over the
first 2.4 m and 5 log10 over the next 27 m. To clarify this nonlinear removal, column
experiments were carried out under similar conditions as in the field: same recharge water,
temperature (5 F 3 jC) and pore water velocity (1.5 m day 1) (Schijven, 2001). Soil
samples were taken along a streamline between the recharge canal and the first monitoring
well. Bacteriophage fX174 was included for comparison. The high initial removal in the
field was found not to be due to heterogeneity of phage suspensions but to soil
heterogeneity. Phage removal rates correlated strongly positively with soil organic carbon
content, and relatively strongly positively with silt content and the presence of ferric
oxyhydroxides (Schijven, 2001). Note that here we are not referring to microscale grain
surface charge heterogeneities but to macroscale spatial heterogeneities.
The experiments reported here were designed to closely simulate field conditions. To
that aim, two different columns were filled with saturated sand from the field. Water from
the recharge canal was used. The experiments were all conducted in a cold room at the same
temperature as that of the groundwater during the field study. The same transport velocity as
in the field (1.5 m day 1) was applied. Presence of physical non-equilibrium was
investigated with the aid of salt breakthrough curves. Also, breakthrough curves of
bacteriophages MS2, PRD1 and fX174 were measured. The latter phage was included
because it is less negatively charged than MS2 and PRD1, and may therefore interact
differently with kinetic sites for attachment. A two-site kinetic model was constructed and
its ability to simulate the breakthrough curves better in comparison to a one-site kinetic
model was studied. The laboratory experiments reported here serve to increase our insight
in the role kinetic adsorption in the modelling of virus removal.
2. Experimental methods
2.1. Microorganisms
Highly concentrated suspensions of MS2 and PRD1 were prepared as described in the
Castricum field study (Schijven et al., 1999). A highly concentrated suspension of fX174
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was prepared as described in ISO 10705-2 (2000b). A portion of each suspension was
diluted with 1 g l 1 peptone –saline to a concentration of 1010 – 1011 phages l 1. These
were used as stock suspensions. Prior to each experiment, aliquots from the stock
suspensions of all three bacteriophages were diluted 1000-fold in a container with canal
water for seeding. MS2 and PRD1 were selected as model viruses because of their negative
charge. MS2 is an icosahedral phage with a diameter of 27 nm and a low isoelectric point
(pI) of 3.5. PRD1 is an icosahedral bacteriophage with a diameter of 62 nm with an inner
lipid membrane (Bales et al., 1991; Caldentey et al., 1990). Its pI lies between 3 and 4
(Loveland et al., 1996). Bacteriophage fX174 has a pI of about 6.6 and a size of 23 nm
(Fujito and Lytle, 1996; Jin et al., 1997).
MS2 and PRD1 are the most hydrophobic viruses, but fX174 exhibits little, if any,
hydrophobic character (Lytle and Routson, 1995; Shields and Farrah, 1987).
2.2. Packing of columns
A sample of about 50 kg of dune sand from the Castricum field site was taken near the
screen of the first monitoring well at a distance of 2.4 m. The sample was kept saturated
with canal water and transported in stainless steel buckets. Samples of canal water were also
collected in 20-l polyvinylchoride containers. The sand and water samples were stored at
5 F 3 jC. Only the sand and water from the field site were used for packing laboratory
columns and performing virus transport experiments.
Fig. 1 shows a schematic representation of a column; a Perspex pipe with an inner
diameter of 9 cm and a length of 1.9 m. A stainless steel grid for supporting the sand
was placed at the bottom of the pipe. A stainless steel table supported the column. Along
the pipe, 14 small stainless steel samplers were placed at 10-cm intervals. The pipe was
filled with saturated dune sand at small increments. During the filling, canal water was
flowing upwards. At the same time, the pipe was being tapped in order to distribute the
sand evenly and to dislodge any air bubbles. The pipe was filled up to a length of 1.5 m.
Initially, a thin layer of very fine sand particles settled on top of the column. This layer
was removed by suction in order to create the same conditions as in Castricum field
experiments. Note that no fine particles were removed during the filling of column.
Thus, any fine particles originally present within the sand stayed behind. After 1 – 2 days,
the flow of water was reversed to downward direction at a rate of 2.4 ml min 1;
resulting in a pore water velocity of about 1.5 m day 1, the same as in the field. The
sand column was kept saturated at all times. The water in the funnel-shaped outlet of the
column was gently, but continuously, mixed by means of a magnetic stirrer. This way,
the concentration gradient at the lower boundary of the column was kept to zero. In all
experiments, pH of the recharge water was 7.5– 8.0. At the inlet, canal water containing
salt or microorganisms were pumped into the inflow reservoir. The overflow kept the
Fig. 1. Schematic representation of a column, filled with sand to a length of 1.5 m. Inner column diameter is 9 cm.
At the inlet canal water was pumped and salt and microorganisms were seeded. The overflow kept the level of
water above the column constant and led excess of water to the feeding tank. The pump that was connected to the
outlet determined the flow rate of water through the column and led the effluent to a disposal tank. Numbers 1 –
14 represent stainless steel samplers, each 10 cm apart.
J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
263
water at a constant head and returned excess water to the feed tank. The pump that was
connected to the outlet regulated the flow rate of water through the column and sent the
effluent to a disposal tank.
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J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
Two columns were prepared. Column I was operated at a pore water velocity of 1.5 m
day 1 and column II at about twice this velocity.
2.3. Salt tracer experiments
For each column that was constructed, a salt transport experiment was carried out to
serve two purposes: (i) to estimate interstitial flow velocity and medium dispersivity and
(ii) to investigate the presence of kinetic effects due to the exchange of solutes between
mobile and immobile regions. First, the water reservoir on top of the column was
emptied by pumping to the point where less than 1 mm of water was left on top of the
column. Then, it was filled gently with a solution of 750 mg l 1 sodium chloride in
canal water up to the level of the overflow. This way, a sharp front of salt water was
introduced into the sand column. The salt solution was fed for a period of 24 h. At the
end of the dosage, the salt solution was replaced by canal water following the same
procedure as at the start of the dosage. All samples were taken from sampler number 14
(at a depth of 1.4 m). Sampling was carried out by continuously pumping from the
sampler at a rate of about 0.2 ml min 1 for 18 min per sample. Samples were collected
in glass tubes using a programmable fraction collector. Concentration of the salt
solution was determined by manually measuring electrical conductivity of the sampled
fractions.
2.4. Transport experiments with bacteriophages
Suspensions of bacteriophages with concentrations of 107 –108 phages l 1 were
seeded for 24 h and breakthrough was monitored for a period of about a week. Seeding
of the phages was carried out following the same procedure as explained for the salt
tracer. Bacteriophages were sampled at sampler number 14 at the depth of 1.4 m at a
rate of 0.2 ml min 1. Samples were collected automatically every 6 min in glass tubes.
Thus, over a period of 7 days, 1680 samples were collected. For each breakthrough
curve of a bacteriophage, about 70 –140 samples were analyzed. The sample collection
tubing consisted of PTFE and silicone. Prior to each experiment, the tubing was rinsed
with a chlorine solution and then with hot tap water. The tubing was tested for
interaction with bacteriophages. This was done by pumping suspensions of bacteriophages through the tubing at a rate of 0.2 ml min 1. Eight replicate influent and effluent
samples were analyzed for bacteriophages. Analysis of variance showed no significant
differences between influent and effluent concentrations. Therefore, we were sure that
no attachment of bacteriophages to the tubing occurred.
2.5. Enumeration of bacteriophages
MS2 was assayed as described in ISO 10705-1 (2000a) using host strain WG49
(Havelaar et al., 1984). PRD1 was assayed according to ISO 10705-1 using S.
typhimurium LT2 as the host, omitting nalidixic acid in the top agar layer. Bacteriophage
fX174 was assayed according to ISO10705-2 (2000) using WG5 (ACTC 700078) as
the host.
J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
265
3. Modeling methods
3.1. Conceptual model
Major processes controlling the transport and removal of viruses in porous media are
advection, dispersion, sorption (attachment and detachment), and inactivation of both free
and adsorbed viruses. Both equilibrium and kinetic models have been used for modeling
sorption of viruses. The role of equilibrium sorption is often found to be negligible
(Schijven and Hassanizadeh, 2000). In fact, most researchers have described sorption of
viruses by a linear kinetic model; that is, linear attachment and linear detachment occurring
at different rates. Commonly, the attachment rate coefficient is much larger than the
detachment rate coefficient. In the Castricum field study, we employed a one-site linear
kinetic sorption model for the simulation of breakthrough curves. Although the breakthrough curve could be simulated reasonably well, there was a significant discrepancy at the
end of the rising limb and at the start of the declining limbs of the breakthrough curves
(Schijven et al., 1999). It was speculated that the presence of more than one type of kinetic
site could be responsible for this shortcoming of the one-site kinetic model. To investigate
whether multiple kinetic sites were present in the Castricum dune sands, a two-site kinetic
model was constructed and used for analyzing bacteriophages breakthrough curves
obtained in laboratory and field experiments. The aim has been to determine whether rate
constants for the two kinetic sites are identifiable. The governing equations for an
advection – dispersion model, including reversible adsorption to two types of kinetic sites
and inactivation of free and attached bacteriophages, in the case of uniform one-dimensional flow, are as follows:
DC qB DS1 qB DS2
D2 C
DC
q
q
þ
ll C ls1 B S1 ls2 B S2
þ
¼ aL v 2 v
Dt
Dx
Dx
n Dt
n Dt
n
n
ð1Þ
qB DS1
q
q
¼ katt1 C kdet1 B S1 ls1 B S1
n Dt
n
n
ð2Þ
qB DS2
q
q
¼ katt2 C kdet2 B S2 ls2 B S2
n Dt
n
n
ð3Þ
where C is concentration of free phages [pfu/m3]; S is concentration of attached phages
[pfu/kg]; t is time [day 1]; x is distance [m]; aL is dispersivity [m]; v is average interstitial
water velocity [m day 1]; qB is dry bulk density [kg/m3]; n is porosity [– ]; katt and kdet are
attachment and detachment rate coefficients, respectively [day 1]; ll and ls are inactivation rate coefficients of free and attached phages, respectively [day 1]. Subscripts 1 and 2
refer to the two different kinetic sites. These equations are subject to boundary conditions
C = C0 at x = 0 and DC/Dx = 0 at x = L. The initial conditions were zero concentration for all
phages.
A numerical model called EQ2KIN was constructed for solving the equations. The
equations were discretized using an explicit central finite difference scheme.
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J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
Fitting of the breakthrough curves was carried out using log-transformed concentrations.
The justification for this choice is as follows. Dilutions of the samples were made to obtain
an approximately constant counting range in each plate. Within each analyzed dilution,
phages are approximately Poisson-distributed. Poisson distribution implies that mean and
variance are the same. Since mean counts were approximately constant, this also applies for
the variance. To obtain concentrations, counts are multiplied by their corresponding
dilution factor. Due to this multiplication, the errors in the observed concentrations will
be approximately constant after log-transformation.
As a measure of goodness-of-fit, the coefficient of determination r2 (Toride et al., 1995)
was calculated on the basis of N logarithmically transformed observations Ci and fitted
values Fi:
N
X
r2 ¼ 1 ðlnCi lnFi Þ2
i¼1
0
N B
X
B
BlnCi B
i¼1 @
N
X
i¼1
12
ð4Þ
lnCi C
C
C
C
N
A
For comparison, a one-site kinetic model was also used for fitting of the breakthrough
curves. To that aim, the same procedure was followed as for fitting of the two-site kinetic
model, but the parameter values for site 2 were set to zero.
Under steady-state conditions, the relative contributions of inactivation and adsorption
to the removal of viruses by soil passage can be computed analytically. A steady-state
situation occurs when input of virus continues for a long time and may be seen as a worstcase situation. For a steady-state situation, Eqs. (1) –(3) are simplified to:
aL v
D2 C
DC
q
q
¼ ll C þ ls1 B S1 þ ls2 B S2
v
2
Dx
Dx
n
n
ð5Þ
qB
katt1
S1 ¼
C
n
ls1 þ kdet1
ð6Þ
qB
katt2
S2 ¼
C
n
ls2 þ kdet2
ð7Þ
Substitution of Eqs. (6) and (7) into Eq. (5) gives:
aL
D2 C DC k
C¼0
Dx2
Dx v
ð8Þ
J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
267
where
k ¼ ll þ
katt1
katt2
þ
1 þ kdet1 =ls1 1 þ kdet2 =ls2
Now, Eq. (8) has the following solution:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
1 þ 4aL kv
C
x
log10
¼
2aL
C0
2:3
ð9Þ
ð10Þ
where C0 is concentration at x = 0, and log(C/C0) is a measure of virus removal.
The term k in Eq. (9) is equivalent to an overall removal rate coefficient. It is evident
from Eq. (9) that three terms contribute to the overall removal rate. The first term is due to
the inactivation of free viruses. The second and last terms give the removal rate of viruses
due to interaction with the two kinetic sites. Interaction means the combination of
attachment, detachment and inactivation of attached viruses. The parameter values obtained
from fitting the breakthrough curves were employed to calculate the removal rates and the
contribution of inactivation and interaction with both kinetic sites under steady-state
conditions.
3.2. Calculation of collision efficiencies
In colloid filtration theory of attachment, the parameter ‘‘collision efficiency’’ is
introduced as a measure of the intrinsic capacity of the soil for adsorption (Yao et al.,
1971). The collision efficiency is an empirical constant that accounts for electrostatic
interactions, in this case, between bacteriophages and the porous medium. Collision
efficiency, a, is calculated using the following equation (Yao et al., 1971):
a¼
2
dc
katt 1
3 ð1 nÞ v g
ð11Þ
where a is collision efficiency, g is single collector efficiency and dc is grain size [m].
Bacteriophages are small in size and their transport in the immediate vicinity of the soil
grains is dominated by Brownian diffusion. Thus, the single collector efficiency g is
determined from the following formula (Penrod et al., 1996):
2=3
g ¼ 4A1=3
s NPe
ð12Þ
where NPe = dpvn/DBM accounts for diffusion, DBM = KB(T + 273)/(3pdpl) is diffusion
coefficient [m2 s 1] with Boltzmann constant KB = 1.38 10 23 (J K 1), dp represents
virus particle size [m] and T is water temperature [jC]. As = 2(1 c5)/(2 3c + 3c5 2c6) is
Happel’s porosity-dependent parameter, with c=(1 n)1/3. Eqs. (11) and (12) were
employed to calculate collision efficiencies a1 and a2, from estimates of katt1 and katt2,
respectively.
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4. Results
4.1. Analysis of salt breakthrough curves
Fig. 2 shows observed and fitted salt breakthrough curves from both columns I and II. As
can be seen, salt behaves as a conservative tracer; a steady-state value of C/C0 = 1 is reached
and excellent fits of the breakthrough curves have been obtained. In addition to the two
column experiments presented here, we did several other salt tracing experiments in other
columns (data not shown). In all of these experiments, salt behaved as a conservative tracer.
In the case of the salt BTC from column II, we see an apparent tailing. But that is most
probably due to drifting of the EC meter as the EC drops below the background value.
Therefore, we may conclude that there are no physical non-equilibrium effects present in
these columns.
Salt breakthrough curves were used to estimate medium porosity and dispersivity.
Corresponding values are listed in Table 1 where also values from Castricum field study are
reported.
4.2. Analysis of phages breakthrough curves
Figs. 3, 5a– 5e show the measured and simulated breakthrough curves in column I. Our
model EQ2KIN was coupled to parameter estimation code PEST version 1.07 (Watermark
Computing, 1994) in order to determine adsorption parameter values from column I
breakthrough curves. Both one-site and two-site kinetic adsorption parameter values were
estimated. These were katt1, katt2, kdet1, kdet2 and ls1. The value of parameter ls2 was
assumed to be equal to ls1. The inactivation rate of phages in water, ll, were found in
another series of experiments (Schijven, 2001) by measuring their inactivation in
Fig. 2. Measured salt breakthrough curves Obs(I) and Obs(II) from column experiments I and II and fitted
breakthrough curves (solid lines).
J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
269
Table 1
Experimental conditions of column experiments and of first two monitoring wells in the Castricum field study,
W1 and W2
Column or well no.
I
II
W1a
W2a
Travel distance [m]
v [m day 1]
aL [m]
1.41
1.6
0.0075
1.42
3.5
0.0043
2.4
1.4
0.0080
3.8
1.6
0.012
a
Data from field study (Schijven et al., 1999). Porosity 0.35.
suspensions made from column influent and effluent samples for a period of 1 –2 weeks.
The estimated ll values were 0.082 day 1 (MS2), 0.044 day 1 (PRD1) and 0.012 day 1
(fX174).
Fig. 3 shows the measured breakthrough curve of MS2 in column I. First, a one-site
kinetic model was applied to fit this curve with the concentrations on a linear scale using
EQ2KIN and setting parameter values for site 2 to zero. Values for katt1, kdet1 and ls1 are
given in Table 2, under heading A, and correspond with curve A in Fig. 3. Curve A fits the
measured breakthrough curve very well except for the tail part. This is not considered as
satisfactory because the tails contain important information on the inactivation rate of
attached phages (Schijven et al., 1999). Indeed, parameter values appear to be unrealistic.
The value of kdet1 is unexpectedly higher than that of katt1 and the value of ls determined
here is 50 times higher than the value of ll. In an analysis of virus inactivation from batch
experiments (Schijven and Hassanizadeh, 2000), it was found that if values of ls were
higher than that of ll, this was usually only by a factor of 2 – 3 and, occasionally, 6 –8. Fig. 4
shows the corresponding residual values, i.e. the differences between observed and fitted
concentrations on log scale. Because the tail of curve A deviates from the measured tail,
residual values of the tail part become increasingly positive.
Fig. 3. Measured breakthrough curve (open circles) of MS2 in column I fitted with a one-site kinetic model
(curves A and B) and a two-site kinetic model (curve C).
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J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
Table 2
Parameter values (in day 1) estimated from breakthrough of MS2 in column III; A, B, and C in column headings
correspond to curves A, B, and C in Fig. 3
Rate coefficients
A: One-site model
B: One-site model
C: Two-site model
katt1
kdet1
katt2
kdet2
ls1 = ls2
4.5
5.0
2.2
0.074
3.9
0.48
2.1
0.054
8.8
42
0.43
In another set of simulations, again a one-site model was used, but this time, we used our
model, EQ2KIN, with log-transformed concentrations and setting the parameter values for
site 2 to zero. The corresponding parameter values are given under heading B of Table 2 and
the corresponding curve B is also shown in Fig. 3. Note that this particular curve was forced
to fit the maximum breakthrough concentration by giving this concentration extra weight;
otherwise, the maximum breakthrough concentration would have been underestimated by
about 0.5log10. This time a perfect fit of the tail is obtained but the same discrepancies that
were observed around the rising and declining limbs of breakthrough curves from the field
study are seen here. These discrepancies are reflected in the residual values in Fig. 4 that are
negative at the rising limb and positive at the declining limb of the breakthrough curve. The
value of kdet1 is now much less than that of katt1.
Finally, the breakthrough curve was fitted by applying the two-site kinetic model. The
estimated values are given under heading C of Table 2. The resulting curve C, in Fig. 3,
clearly gives a very satisfactory fit to the measurements. This is also reflected by the
corresponding residual values in Fig. 4, which are randomly scattered around zero, with an
average residual of 0.0036 and a variance as small as 0.12. This implies that the
assumption of log-normally distributed concentrations is reasonable. The height of the
breakthrough curve is mainly determined by the values of katt1, katt2, kdet2 and ll. The
skewness of the rising and declining limbs is strongly affected by the value of kdet2. After
Fig. 4. Residual values (observed minus fitted values) on log-scale corresponding to models A, B and C in Fig. 3.
J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
271
the pulse of viruses has passed, site 2 looses its influence on the shape of the curve because
of the high detachment rate of this site. The tail of the breakthrough curve is mainly
determined by the values of kdet1 and ls1. Because the detachment rate from site 2 is
relatively fast, there is little effect of inactivation of viruses that are attached to site 2.
Consequently, estimates of ls2 may not be meaningful. It was believed to be a reasonable
assumption to set ls2 equal to ls1; this was done in all of our simulations.
Figs. 3, 5a and 5b give the fitted breakthrough curves of MS2, PRD1 and fX174,
respectively, in column I. Corresponding parameter values are given in Table 3. Parameters
of the one-site model for MS2 and PRD1 have similar values. In the case of PRD1, the tail
of the breakthrough curve appears to be curved and becomes flatter at the end. The one-site
model does not follow this trend, whereas the two-site model does fit the slight bend of the
tail. Compared to MS2, the values of katt2 and kdet2 for PRD1 are smaller. The estimate of ls
for PRD1 is now much smaller compared to the one-site model; it is only 50% greater than
the ll value for PRD1. This is in agreement with the literature where the value of ls is found
to be equal or slightly higher than that of ll (Blanc and Nasser, 1996; Schijven and
Hassanizadeh, 2000). However, the value of ls for MS2 is found to be about five times
higher than the value of its ll. This is probably overestimated. Also, the values of katt2 and
kdet2 are quite high and are most probably overestimated.
The breakthrough curve of fX174 is very much skewed to the right (Fig. 5b). The onesite model fits this curve badly, but the two-site model fits it very well. The goodness-of-fit
(r2) of the two-site model for fX174 was a bit lower than for MS2 and PRD1. Probably, the
reason is that the counts of fX174 in the samples from the tail of the breakthrough curve
were relatively low, resulting in a large variation in the observed concentrations.
Consequently, it was difficult to get a reliable fit of the tail. Bacteriophage fX174 is
relatively stable. Therefore, it was assumed that the inactivation coefficient of attached
fX174 has the same value as that of free fX174. The curvature of its breakthrough tail is
similar to that of PRD1, which is followed well by the two-site model.
All three bacteriophages attach relatively fast to site 1 and detach very slowly from this
site, whereas both attachment to and detachment from site 2 are fast. Consequently, the
removal rate coefficient k is mainly determined by interaction with site 1, and only for a
minor part by interaction with site 2.
The fact that the two-site model gives a better visual fit of the breakthrough curves is
supported by the higher goodness-of-fit values for the two-site model than for the one-site
model, although in the case of PRD1 this difference is small.
So far, estimates of model parameters had been obtained by fitting the observed
breakthrough concentrations. This way, it appeared that a two-site kinetic model gives a
better description of the breakthrough curves than a one-site kinetic model. In order to
evaluate the two-site model further, parameter values obtained from column I breakthrough curves were used to predict the breakthrough curves from column II. The flow
velocity in this column was 2.2 times higher than in column I. According to the colloid
filtration theory (Yao et al., 1971), katt1 is proportional to v1/3. Therefore, katt1 was
increased by a factor 1.3. So, values of kdet1, katt2, kdet2, ll, ls1 and ls2 were kept
constant, but the value of katt1 was adjusted by a factor of 1.3. This simulation was
carried out applying both the one- and two-site kinetic models. Figs. 5c, 5d and 5e
show the predicted breakthrough curves.
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J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
In the case of MS2, both one- and two-site kinetic models slightly under-predict the
maximum breakthrough concentration, and also the tail is lower. Both model predictions
are in fact very similar. This is probably due to the fact that the tail of the breakthrough
curve of MS2 in column I was straight. The prediction of the PRD1 breakthrough by the
two-site model is very good, except for the discrepancy at the very end of the tail. The onesite model prediction and shows discrepancies at the beginning and the end of the tail of the
breakthrough curve. In the case of fX174, the maximum breakthrough concentration is
Fig. 5. (a) – (e) Breakthrough curves of bacteriophages. Circles are observations. The solid lines are the one- and
two-site kinetic model fit. The dotted lines are the one- and two-site model predictions. In column II two times
higher pore water velocity than in column I. (a) PRD1 in column I. (b) fX174 in column I. (c) MS2 in column II.
(d) PRD1 in column II. (e) fX174 in column II.
J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
273
Fig. 5 (continued ).
under-predicted by the two-site kinetic model, but it roughly follows the curvature of the
tail. The prediction by the one-site kinetic model shows large discrepancies at the rising
limb and at the beginning of the tail of the breakthrough curve.
Overall, predictions by the two-site kinetic model were reasonably good considering the
goodness-of-fits between the predicted and observed concentrations, i.e. 84% (MS2), 89%
(PRD1) and 75% (fX174). However, the same may be said for the predictions by the onesite model for MS2 and PRD1 with goodness-of-fits of 86% and 93%, respectively. The
goodness-of-fit for the prediction of the fX174 breakthrough curve with one-site kinetic
was much lower, 34%. This is mainly due to the strong skewness of the rising and declining
limbs of the fX174 breakthrough curve.
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J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
Fig. 5 (continued ).
As an additional exercise, we fitted breakthrough curves of column II in order to obtain
best-fit values of parameters of both models. Also, the 95% confidence intervals were
determined. Results are given in Table 3. The fitted breakthrough curves are shown in Figs.
5c, 5d and 5e. Note that the dispersivities from columns I and II differed by almost a factor
two (Table 1). This difference is probably due to some difference in packing of the columns.
Nevertheless, these dispersivities are so low that they had little effect on fitting and
simulation results. By applying dispersivity ranging from 4 to 16 mm, it was found that the
fitted values of adsorption parameters did not change more than 5%.
We have found that in the case of MS2 and PRD1, for both one-site and two-site models,
the predicted values of katt1 for column II (1.3 times the value of katt1 from the experiment
with column I) fall within the 95% confidence interval of the best estimates of katt1. In the
case of fX174, the predicted values of katt1 fall just outside this 95% confidence interval.
This suggests that our observations are consistent with the colloid filtration theory, which
prescribes an increase in katt1 with a factor of 21/3, i.e. 1.3 as a result at twice the velocity.
This is also reflected in the best-fit values of the collision efficiency of site 1, a1, which are
more or less the same for both columns, for a given bacteriophage (compare values of a1 for
each bacteriophage under two-site model in Table 3).
Another interesting observation is that the values of katt2, kdet2 and ls for MS2 are now
much smaller (compared to the values obtained from column I) and seem to be more
realistic. The values of ls are almost the same as ll, just as what one would expect (Blanc
and Nasser, 1996; Schijven and Hassanizadeh, 2000). As can be seen in Fig. 5c, the tail of
Notes to Table 3:
Dimension of parameters is day 1. The values of ls1 and ls2 for fX174 were set equal to that of ll.
The estimated ll values were 0.082 day 1 (MS2), 0.044 day 1 (PRD1) and 0.012 day 1 (fX174).
The 95% confidence intervals are given between brackets.
Table 3
Parameter values from fitting breakthrough curves of bacteriophages in columns I and II
Bacteriophage
Column I
Column II
fX174
MS2
PRD1
fX174
2.2 (2.1 – 2.4)
0.074 (0.050 – 0.11)
0.48 (0.40 – 0.58)
0.0010
80%
2.0
4.1%
95.9%
1.1
0.55
0.86
2.0 (1.97 – 2.12)
0.085 (0.075 – 0.096)
0.47 (0.36 – 0.60)
0.0012
95%
1.8
2.5%
97.5%
1.2
0.48
0.76
7.0 (6.3 – 7.8)
0.0039 (0.0031 – 0.0050)
0.012
0.0023
–
5.3
0.2%
99.8%
1.4
1.4
2.2
2.5 (1.8 – 3.4)
0.14 (0.098 – 0.020)
0.48 (0.37 – 0.61)
0.00061
96%
2.0
4.2%
95.8%
1.2
0.25
0.86
2.5 (2.2 – 2.8)
0.089 (0.081 – 0.098)
0.40 (0.33 – 0.47)
0.0011
95%
2.1
2.1%
97.9%
1.2
0.26
0.91
10 (9.7 – 10.5)
0.046 (0.040 – 0.053)
0.53 (0.31 – 0.89)
0.0023
90%
9.3
0.1%
99.9%
1.1
1.2
4.0
Two-site model
katt1
kdet1
katt2
kdet2
ls1 = ls2
a1
a2
r2
k
% ll
% s1
% s2
katt1/k
log10(C/C0)/x
log10(C/C0)/t
2.1 (1.8 – 2.4)
0.054 (0.045 – 0.065)
8.8 (6.5 – 12)
42 (29 – 61)
0.43 (0.39 – 0.47)
0.00068
0.0028
96%
2.0
4.0%
91.5%
4.4%
1.0
0.56
0.87
1.9 (1.83 – 1.94)
0.0045 (0.0036 – 0.0055)
0.47 (0.41 – 0.53)
1.1 (0.97 – 1.3)
0.064 (0.044 – 0.092)
0.0011
0.00027
98%
1.8
2.4%
96.2%
1.4%
1.0
0.50
0.79
8.0 (7.0 – 9.2)
0.0028 (0.0018 – 0.0045)
2.2 (1.4 – 3.7)
1.2 (2.3 – 4.1)
0.012
0.0024
0.00086
83%
6.5
0.2%
99.6%
0.2%
1.2
1.8
2.8
2.1 (1.4 – 2.9)
0.016 (0.011 – 0.023)
0.63 (0.58 – 0.70)
1.4 (1.3 – 1.5)
0.075 (0.060 – 0.094)
0.00051
0.00016
97%
1.8
4.5%
93.6%
1.9%
1.1
0.23
0.78
2.2 (2.0 – 2.3)
0.017 (0.016 – 0.018)
0.48 (0.44 – 0.53)
1.6 (1.5 – 1.8)
0.065 (0.058 – 0.072)
0.00097
0.00021
98%
1.8
2.4%
96.5%
1.0%
1.2
0.22
0.77
9.5 (9.3 – 9.8)
0.0031 (0.0026 – 0.0037)
0.72 (0.63 – 0.83)
0.96 (0.85 – 1.1)
0.012
0.0022
0.00016
91%
7.6
0.2%
99.7%
0.1%
1.2
0.95
3.3
275
PRD1
J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
MS2
One-site model
katt1
kdet1
ls1
a1
r2
k
% ll
% s1
katt1/k
log10(C/C0)/x
log10(C/C0)/t
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J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
MS2 appears to flatten at the end (this was not the case in column I) and this is probably the
reason that a lower value of ls is obtained.
Again, we see a much better visual fit of the breakthrough curves, especially of the
curved tails, by the two-site model as compared to the one-site model. Nevertheless, the
goodness-of-fit values found from fitting with the two-site model are only a few percent
higher than with the one-site model.
Column experiments were carried out at low temperature (5 F 3 jC), at which
inactivation rates are low. As can be seen in Table 3 (see rows starting with E and
under), interaction with site 1 accounts for 92– 97% of removal of MS2 and PRD1
and for almost 100% for removal of fX174. Because katt1Hkdet1, it follows from Eq.
(9) that k c katt1, meaning that katt1 is the most important parameter for the removal of
viruses at low temperatures. In other words, if one were interested in overall removal
of viruses, a one-site kinetic model would be adequate for all practical purposes.
Predicted removal with travel distance ( log10(C/C0)/x) at twice the pore water
velocity in column II is about half that in column I. Removal with travel time
( log10(C/C0)/t) is hardly affected by pore water velocity, as one would expect.
5. Discussion and conclusions
The laboratory experiments reported here serve to gain insight in the kinetic modeling of
breakthrough curves of viruses. One-site and two-site kinetic models have been employed.
Breakthrough curves could be fitted and predicted satisfactorily by a two-site kinetic model,
but not by a one-site kinetic model. Breakthrough curves that appear to be very skewed to the
right, like that of fX174, are fitted poorly by a one-site kinetic model but a good fit is
obtained using a two-site kinetic model. We contend that similarly shaped breakthrough
curves reported for bacteriophages (Bales et al., 1991, 1993; DeBorde et al., 1998, 1999;
Dowd et al., 1998), bacteria (Hornberger et al., 1992; Johnson et al., 1995; Lindqvist et al.,
1994; McCaulou et al., 1994; Tan et al., 1994), Cryptosporidium (Harter et al., 2000) and
colloidal particles (van de Weerd et al., 1998) can be satisfactorily simulated using a two-site
kinetic model.
Tails of breakthrough curves that are measured long enough are not straight on a
semi-log scale but curve up. Such tails cannot be simulated by a one-site model. In
MS2 breakthrough curve of column I, this flattening of the tail of the breakthrough
curve was not clearly observed, leading to about five times higher estimates of ls.
Apparently, it is important to continue measurement of the breakthrough tails long
enough to get a good estimate of ls. In column II, more pore volumes passed the
column (about 14 pore volumes in 7 days) than in column I (about 10 pore volumes
in 10 days). Thus, tails that are measured too short may lead to an overestimation of
ls. This also leads to an overestimation of the values of katt2 and kdet2. It must be
emphasized that an overestimation of ls always occurs if a one-site kinetic model is
applied.
Although the two-site model fits the breakthrough curves better than the one-site
model, leading to more accurate estimation of values of adsorption and inactivation
parameters, we have found that overall removal rates predicted by either model are very
J.F. Schijven et al. / Journal of Contaminant Hydrology 57 (2002) 259–279
277
similar. That is to say, interaction with kinetic site 2, under the assumption that ls2
equals ls1, only has a minor contribution to overall removal. Generally, katt1Hkdet1,
katt2 V kdet2 and katt2 < katt1.
The value of katt1 for fX174 were found to be higher than those for MS2 and
PRD1. A similar difference in values of adsorption coefficients was also found
between MS2 and fX174 in Ottawa sand at pH 7.5 by Jin et al. (1997, 2000). This
is mainly due to the fact at pH 7.5 – 8.0, the dune sand is predominantly negatively
charged and conditions are unfavorable for attachment to negatively charged viruses.
Under such unfavorable conditions for attachment, the virus – grain interaction is the
rate-limiting step for attachment and not the transport to the site by diffusion (Ryan
and Elimelech, 1996). MS2 and PRD1 experience a greater electrostatic repulsion than
the less negatively charged fX174, and thus adsorb less to site 1.
With some exceptions, values of katt2 and kdet2 for all bacteriophages were of the
same order of magnitude, despite the differences that exist in hydrophobicity and
surface charge between the bacteriophages. This suggests that the nature of their
interaction with sites of type 2 is neither electrostatic nor hydrophobic. Based on the
shape of the salt breakthrough curves, we may exclude the so-called physical nonequilibrium effects, like distribution between mobile and immobile regions of water.
The actual nature of the adsorption site 2 remains yet to be determined.
Another issue that could have affected our results is the aggregation of viruses.
Although, this cannot be excluded with certainty, we believe it is most unlikely to
have occurred in our case. Aggregation of phages has been discussed by Grant
(1994), who applies a worst case where every collision of a phage particle with
another phage particle would result in aggregation, which is unlikely considering their
opposite charges. Only in lab stocks of 1012 pfu/ml, significant aggregation may
occur. At 105 pfu/ml, used in our experiments, it is not expected to happen. Even if
aggregates have formed in the cultured stock, they are most probably dispersed in the
course of washing (with chloroform) and dilution. Moreover, the linearity of phage
removal as a function of travel distance within a column, as well as the observed first
order course of inactivation (Schijven, 2001), suggest that the existence of aggregates
of phages is insignificant. Another strong indication is that no differences were seen
using freshly prepared or 2-year-old phage suspensions (Schijven, 2001). In any case,
the existence of phage aggregates cannot explain the curvature of the tail of the
breakthrough curve.
Acknowledgements
This work was funded by the Ministry of Housing, Physical Planning and the
Environment under project 289202, Water Microbiology.
W. Hoogenboezem and J. Bergsma (PWN Water Supply North Holland, The
Netherlands) are greatly acknowledged for their support in obtaining sand samples, soil
and water analyses. L.C. Rietveld and M. v.d. Meulen (Delft University of Technology)
are thanked for the design and construction of the Perspex column supports.
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